Measurements in Relativistic Quantum Mechanics

Abstract

Abstract This chapter develops the theory of measurements in relativistic quantum mechanics. The presentation is based on the idea to consider the state of a relativistic quantum system as a functional on the set of space-like hypersurfaces in Minkowski space. This idea leads to a manifest covariant time-evolution equation, known as Schwinger–Tomonaga equation, and allows a relativistic formulation of the projection postulate of quantum measurement theory. This postulate is used to study a number of applications to local and non-local measurements, to the erasing of local information, and to the restrictions on the measurability of non-local quantities imposed by the causality principle. The relativistic projection postulate further enables the discussion of many important problems from a unified perspective, such as EPR-type experiments, measurements of Bell state operators, exchange measurements, and quantum teleportation.